Astudent sits at rest on a piano stool that can rotate without friction. the moment of inertia of the student-stool system is 4.5 kg⋅m2 . a second student tosses a 2.0 kg mass with a speed of 2.5 m/s to the student on the stool, who catches it at a distance of 0.35 m from the axis of rotation. what is the resulting angular speed of the student and the stool?

To place a communications satellite into a geosynchronous orbit at an altitude of 22,240 mi above the surface of the earth, the satellite first is released from a space shuttle , which is in a circular orbit at an altitude of 185 mi, and then is propelled by an upper-stage booster to its final altitude. as the satellite passes through a, the booster's motor is fired to insert the satellite into an elliptic transfer orbit. the booster is again fired at b to insert the satellite into a geosynchronous orbit. knowing that the second firing increases the speed of the satellite by 4810ft/s, determine (a.) the speed of the satellite as it approaches b on the elliptic transfer orbit, (b.) the increase in speed resulting from the first firing at a.